Several Complex Variables Part 1
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Several Complex Variables
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Author : H. Grauert
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Several Complex Variables written by H. Grauert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The present book grew out of introductory lectures on the theory offunctions of several variables. Its intent is to make the reader familiar, by the discussion of examples and special cases, with the most important branches and methods of this theory, among them, e.g., the problems of holomorphic continuation, the algebraic treatment of power series, sheaf and cohomology theory, and the real methods which stem from elliptic partial differential equations. In the first chapter we begin with the definition of holomorphic functions of several variables, their representation by the Cauchy integral, and their power series expansion on Reinhardt domains. It turns out that, in l:ontrast ~ 2 there exist domains G, G c en to the theory of a single variable, for n with G c G and G "# G such that each function holomorphic in G has a continuation on G. Domains G for which such a G does not exist are called domains of holomorphy. In Chapter 2 we give several characterizations of these domains of holomorphy (theorem of Cartan-Thullen, Levi's problem). We finally construct the holomorphic hull H(G} for each domain G, that is the largest (not necessarily schlicht) domain over en into which each function holomorphic on G can be continued.
Functions Of One Complex Variable
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Author : J.B. Conway
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Functions Of One Complex Variable written by J.B. Conway and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is intended as a textbook for a first course in the theory of functions of one complex variable for students who are mathematically mature enough to understand and execute E - I) arguments. The actual pre requisites for reading this book are quite minimal; not much more than a stiff course in basic calculus and a few facts about partial derivatives. The topics from advanced calculus that are used (e.g., Leibniz's rule for differ entiating under the integral sign) are proved in detail. Complex Variables is a subject which has something for all mathematicians. In addition to having applications to other parts of analysis, it can rightly claim to be an ancestor of many areas of mathematics (e.g., homotopy theory, manifolds). This view of Complex Analysis as "An Introduction to Mathe matics" has influenced the writing and selection of subject matter for this book. The other guiding principle followed is that all definitions, theorems, etc.
Several Complex Variables Part 1
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Author : Raymond O'Neil Wells
language : en
Publisher: American Mathematical Soc.
Release Date : 1977
Several Complex Variables Part 1 written by Raymond O'Neil Wells and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Mathematics categories.
Contains sections on Singularities of analytic spaces, Function theory and real analysis, Compact complex manifolds, and Survey papers.
Analytic Functions Of Several Complex Variables
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Author : Robert Clifford Gunning
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Analytic Functions Of Several Complex Variables written by Robert Clifford Gunning and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. This title intends to provide an extensive introduction to the Oka-Cartan theory and some of its applications, and to the general theory of analytic spaces.
Introduction To Complex Analysis In Several Variables
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Author : Volker Scheidemann
language : en
Publisher: Springer Nature
Release Date : 2023-04-26
Introduction To Complex Analysis In Several Variables written by Volker Scheidemann and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-26 with Mathematics categories.
This book gives a comprehensive introduction to complex analysis in several variables. While it focusses on a number of topics in complex analysis rather than trying to cover as much material as possible, references to other parts of mathematics such as functional analysis or algebras are made to help broaden the view and the understanding of the chosen topics. A major focus are extension phenomena alien to the one-dimensional theory, which are expressed in the famous Hartog's Kugelsatz, the theorem of Cartan-Thullen, and Bochner's theorem. The book aims primarily at students starting to work in the field of complex analysis in several variables and instructors preparing a course. To that end, a lot of examples and supporting exercises are provided throughout the text. This second edition includes hints and suggestions for the solution of the provided exercises, with various degrees of support.
Several Complex Variables Vii
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Author : H. Grauert
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Several Complex Variables Vii written by H. Grauert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Of making many books there is no end; and much study is a weariness of the flesh. Eccl. 12.12. 1. In the beginning Riemann created the surfaces. The periods of integrals of abelian differentials on a compact surface of genus 9 immediately attach a g dimensional complex torus to X. If 9 ~ 2, the moduli space of X depends on 3g - 3 complex parameters. Thus problems in one complex variable lead, from the very beginning, to studies in several complex variables. Complex tori and moduli spaces are complex manifolds, i.e. Hausdorff spaces with local complex coordinates Z 1, ... , Zn; holomorphic functions are, locally, those functions which are holomorphic in these coordinates. th In the second half of the 19 century, classical algebraic geometry was born in Italy. The objects are sets of common zeros of polynomials. Such sets are of finite dimension, but may have singularities forming a closed subset of lower dimension; outside of the singular locus these zero sets are complex manifolds.
Elementary Theory Of Analytic Functions Of One Or Several Complex Variables
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Author : Henri Cartan
language : en
Publisher: Courier Corporation
Release Date : 2013-04-22
Elementary Theory Of Analytic Functions Of One Or Several Complex Variables written by Henri Cartan and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-22 with Mathematics categories.
Basic treatment includes existence theorem for solutions of differential systems where data is analytic, holomorphic functions, Cauchy's integral, Taylor and Laurent expansions, more. Exercises. 1973 edition.
Tasty Bits Of Several Complex Variables
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Author : Jiri Lebl
language : en
Publisher: Lulu.com
Release Date : 2016-05-05
Tasty Bits Of Several Complex Variables written by Jiri Lebl and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-05 with Science categories.
This book is a polished version of my course notes for Math 6283, Several Complex Variables, given in Spring 2014 and Spring 2016 semester at Oklahoma State University. The course covers basics of holomorphic function theory, CR geometry, the dbar problem, integral kernels and basic theory of complex analytic subvarieties. See http: //www.jirka.org/scv/ for more information.
Methods Of The Theory Of Functions Of Many Complex Variables
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Author : Vasiliy Sergeyevich Vladimirov
language : en
Publisher: Courier Corporation
Release Date : 2007-01-01
Methods Of The Theory Of Functions Of Many Complex Variables written by Vasiliy Sergeyevich Vladimirov and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.
This systematic exposition outlines the fundamentals of the theory of single sheeted domains of holomorphy. It further illustrates applications to quantum field theory, the theory of functions, and differential equations with constant coefficients. Students of quantum field theory will find this text of particular value. The text begins with an introduction that defines the basic concepts and elementary propositions, along with the more salient facts from the theory of functions of real variables and the theory of generalized functions. Subsequent chapters address the theory of plurisubharmonic functions and pseudoconvex domains, along with characteristics of domains of holomorphy. These explorations are further examined in terms of four types of domains: multiple-circular, tubular, semitubular, and Hartogs' domains. Surveys of integral representations focus on the Martinelli-Bochner, Bergman-Weil, and Bochner representations. The final chapter is devoted to applications, particularly those involved in field theory. It employs the theory of generalized functions, along with the theory of functions of several complex variables.
Several Complex Variables And Complex Manifolds
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Author : Mike Field
language : en
Publisher: Cambridge University Press
Release Date : 1982
Several Complex Variables And Complex Manifolds written by Mike Field and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Complex manifolds categories.
Annotation This self-contained and relatively elementary introduction to functions of several complex variables and complex (especially compact) manifolds is intended to be a synthesis of those topics and a broad introduction to the field. Part I is suitable for advanced undergraduates and beginning postgraduates whilst Part II is written more for the graduate student. The work as a whole will be useful to professional mathematicians or mathematical physicists who wish to acquire a working knowledge of this area of mathematics. Many exercises have been included and indeed they form an integral part of the text. The prerequisites for understanding Part I would be met by any mathematics student with a first degree and together the two parts provide an introduction to the more advanced works in the subject.